SU(2)$_{\tiny\mbox{CMB}}$ at high redshifts and the value of $H_0$

Abstract

We investigate a high-$z$ cosmological model to compute the co-moving sound horizon $r_s$ at baryon-velocity freeze-out towards the end of hydrogen recombination. This model assumes a replacement of the conventional CMB photon gas by deconfining SU(2) Yang-Mills thermodynamics, three flavours of massless neutrinos ($N_{\nu }=3$), and a {\sl purely baryonic} matter sector (no cold dark-matter (CDM)). The according SU(2) temperature-redshift relation of the CMB is contrasted with recent measurements appealing to the thermal Sunyaev-Zel'dovich effect and CMB-photon absorption by molecular rotations bands or atomic hyperfine levels. Relying on a realistic simulation of the ionization history throughout recombination, we obtain $z_{\ast }=1693.55\pm 6.98$ and $z_{\mathrm{drag}}=1812.66\pm 7.01$. Due to considerable widths of the visibility functions in the solutions to the associated Boltzmann hierarchy and Euler equation we conclude that $z_{\ast }$ and $z_{\mathrm{drag}}$ over-estimate the redshifts for the respective photon and baryon-velocity freeze-out. Realistic decoupling values turn out to be $z_{\mathrm{lf},\ast }=1554.89\pm 5.18$ and $z_{\mathrm{lf},\mathrm{drag}}=1659.30\pm 5.48$. With $r_s(z_{\mathrm{lf},\mathrm{drag}})=(137.19\pm 0.45)$Mpc and the essentially model independent extraction of $r_s\cdot H_0=\mbox{const}$ from low-$z$ data in arXiv:1607.05617 we obtain a good match with the value $H_0=(73.24\pm 1.74)$km\,s${}^{-1}$\,Mpc${}^{-1}$ extracted in arXiv:1604.01424 by appealing to Cepheid calibrated SNe~Ia, new parallax measurements, stronger constraints on the Hubble flow, and a refined computation of distance to NGC4258 from maser data. We briefly comment on a possible interpolation of our high-$z$ model, invoking percolated and unpercolated U(1) topological solitons of a Planck-scale axion field, to the phenomenologically successful low-$z$ $\Lambda$CDM cosmology.

14 pages, 9 figures, 3 tables; v3: substantially revised, accepted at Monthly Notices of The Royal Astronomical Society

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• Cosmological parameters from Planck data in SU(2)${}_{\mathrm{CMB}}$, their local $\Lambda$CDM values, and the modified photon Boltzmann equation
• Cosmic Microwave Background as a thermal gas of SU(2) photons: Implications for the high-z cosmological model and the value of $H_0$
• CRPropa 3.2: a public framework for high-energy astroparticle simulations
• SU(2) Yang-Mills thermodynamics: a priori estimate and radiative corrections
• SU(2) Quantum Yang-Mills Thermodynamics: Some Theory and Some Applications